We used SPEX v3.06 [1]}, [2]} for the spectral analysis. Because most of our objects have a temperature \(k_\mathrm {B}T>2\)  keV based on the \(M-k_\mathrm {B}T\)  scaling relations [3]}, we used the atomic database SPEXACT v2.07, which includes fewer lines for a fast calculation. We used the spectral model combination \(cie1\times red\times abs+cie2\times abs+pow\) , where the two \(cie\) s are collisional ionization equilibrium models for the icm and the foreground Galactic halo, \(red\)  is the redshift of the object, \(abs\)  is the Galactic absorption, \(pow\)  is the power law for the cxb. For \(cie1\) , the abundances of metal elements are coupled to Fe, and we set the lower limit to 0.3 proto-solar [4]}. The temperature for \(cie2\)  was fixed to 0.2 keV [5]}, and the normalization of \(abs\)  was set to the value from the database nhtothttps://www.swift.ac.uk/analysis/nhtot/index.php [6]}. The photon index of \(pow\)  was fixed to 1.41 [7]}. We binned the spectra using the optimal binning algorithm [8]} and used the energy range 0.7–7.0 keV for the spectral fitting. The Cash statistics [9]} was adopted to calculate the likelihood when the parameters were optimized.
